Related papers: Cube vs. Cube Low Degree Test
I show that in low dimensions the interactions in dilute Bose mixtures are strongly renormalized, which leads to a considerable change of stability conditions compared to the mean-field results valid in the high-density regime. Estimates…
This paper establishes a statistical versus computational trade-off for solving a basic high-dimensional machine learning problem via a basic convex relaxation method. Specifically, we consider the {\em Sparse Principal Component Analysis}…
Understanding statistical inference under possibly non-sparse high-dimensional models has gained much interest recently. For a given component of the regression coefficient, we show that the difficulty of the problem depends on the sparsity…
An element $a$ of a lattice cups to an element $b > a$ if there is a $c < b$ such that $a \cup c = b$. An element of a lattice has the cupping property if it cups to every element above it. We prove that there are non-zero honest elementary…
In this paper I uncover and explain---using contour integrals and residues---a connection between cubic splines and a popular compact finite difference formula. The connection is that on a uniform mesh the simplest Pad\'e scheme for…
We propose a general methodology for testing whether a given polynomial with integer coefficients is identically zero. The methodology evaluates the polynomial at efficiently computable approximations of suitable irrational points. In…
A robust minimax test for two composite hypotheses, which are determined by the neighborhoods of two nominal distributions with respect to a set of distances - called $\alpha-$divergence distances, is proposed. Sion's minimax theorem is…
Fusing outputs from automatic speaker verification (ASV) and spoofing countermeasure (CM) is expected to make an integrated system robust to zero-effort imposters and synthesized spoofing attacks. Many score-level fusion methods have been…
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
A group $G$ has cube-free order if no prime to the third power divides $|G|$. We describe an algorithm that given two cube-free groups $G$ and $H$ of known order, decides whether $G\cong H$, and, if so, constructs an isomorphism $G\to H$.…
Combinatorial discrepancy is a complexity measure of a collection of sets which quantifies how well the sets in the collection can be simultaneously balanced. More precisely, we are given an n-point set $P$, and a collection $\mathcal{F} =…
A polynomial identity testing algorithm must determine whether an input polynomial (given for instance by an arithmetic circuit) is identically equal to 0. In this paper, we show that a deterministic black-box identity testing algorithm for…
COBE-normalized flat (matter plus cosmological constant) and open Cold Dark Matter (CDM) models are tested by comparing their expected Hubble flow variations and the observed variations in a Type Ia supernova sample and a Tully Fisher…
Exact tests greatly improve the analysis of contingency tables when marginals are low. For instance, researchers often use Fisher's exact test, which is conditional, or Barnard's test, which is unconditional but needs to deal with a…
We introduce the hemicubic codes, a family of quantum codes obtained by associating qubits with the $p$-faces of the $n$-cube (for $n>p$) and stabilizer constraints with faces of dimension $(p\pm1)$. The quantum code obtained by identifying…
We investigate the dimensionality of bipartite quantum systems by construction of a device-independent null witness test. This test assesses whether a given bipartite state conforms with the expected quantum dimension, Schmidt number, and…
A subset $S$ of the Boolean hypercube $\mathbb{F}_2^n$ is a sumset if $S = \{a + b : a, b\in A\}$ for some $A \subseteq \mathbb{F}_2^n$. Sumsets are central objects of study in additive combinatorics, featuring in several influential…
We present subquadratic algorithms, in the algebraic decision-tree model of computation, for detecting whether there exists a triple of points, belonging to three respective sets $A$, $B$, and $C$ of points in the plane, that satisfy a…
This article presents a technique for proving problems hard for classes of the polynomial hierarchy or for PSPACE. The rationale of this technique is that some problem restrictions are able to simulate existential or universal quantifiers.…
Any classifier can be "smoothed out" under Gaussian noise to build a new classifier that is provably robust to $\ell_2$-adversarial perturbations, viz., by averaging its predictions over the noise via randomized smoothing. Under the…